Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
358 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 34. #6226 | Q8 | semidirect |
| 164. C3×C9 | #475 | semidirect |
| 235. C9 | #4851 | semidirect |
| 264. C3 | #10588767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6226 | 2 |
| C9×#869 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720269 | 2 |
| #11720264 | 2 |
| #10590307 | 3 |
| #10588767 | 3 |